Dynamical symmetry of the Kaluza-Klein monopole

TL;DR

This paper reviews the dynamical symmetries of the Kaluza-Klein monopole, showing how classical conserved quantities lead to conic trajectories and how algebraic structures determine spectra and scattering, extending to o(4,2).

Contribution

It provides a comprehensive analysis of the symmetry algebra of the Kaluza-Klein monopole, connecting classical and quantum properties with algebraic methods.

Findings

Classical trajectories are conic sections due to conserved angular momentum and Runge-Lenz vector.

The o(4) algebra enables calculation of bound-state spectra.

The o(3,1) algebra determines the scattering matrix.

Abstract

The Kepler-type dynamical symmetries of the Kaluza-Klein monopole are reviewed. At the classical level, the conservation of the angular momentum and of a Runge-Lenz vector imply that the trajectories are conic sections. The o(4) algebra allows us to calculate the bound-state spectrum, and the o(3,1) algebra yields the scattering matrix. The symmetry algebra extends to o(4,2).